Current methods of chemical vapour deposition (CVD) of graphene on copper are complicated by multiple processing steps and by high temperatures required in both preparing the copper and inducing subsequent film growth. Here we demonstrate a plasma-enhanced CVD chemistry that enables the entire process to take place in a single step, at reduced temperatures (<420 °C), and in a matter of minutes. Growth on copper foils is found to nucleate from arrays of well-aligned domains, and the ensuing films possess sub-nanometre smoothness, excellent crystalline quality, low strain, few defects and room-temperature electrical mobility up to (6.0±1.0) × 10(4) cm(2) V(-1) s(-1), better than that of large, single-crystalline graphene derived from thermal CVD growth. These results indicate that elevated temperatures and crystalline substrates are not necessary for synthesizing high-quality graphene.